Question

PROVE\quad THAT\quad 2{ n }^{ 2 }\ge { (n+1) }^{ 2 }\quad for\quad n\ge 3\quad mathematical\quad analysis\quad problem.

Answer 1

\[PROVE\quad THAT\quad 2{ n }^{ 2 }\ge { (n+1) }^{ 2 }\quad for\quad n\ge 3\quad mathematical\quad analysis\quad problem.\]

Answer 2

I'm tempted to say induction... are we allowed?

Answer 3

this is a mathematical analysis problem.

Answer 4

yes it is, induction is allowed.

Answer 5

Well, first, show that it holds for n = 3.

Answer 6

yes i have done that i got 18>16.

Answer 7

Now, assume it holds for n = k, where k is some integer greater than or equal to 3.
That is to say, this statement
\[\Large 2k^2 \ge (k+1)^2 \qquad k\ge3\] is true.

Answer 8

ok.

Answer 9

now we have to show that it is true for (k+1) term right ?

Answer 10

that's right :)
Try it ^_^

Answer 11

we get 2